Recently, we have introduced [1]} and modified [2]} two graph-decomposition theorems based on a new graph product, motivated by applications in the context of synchronising periodic real-time processes, in particular in the field of robotics.
More on the background, definitions and applications can be found in two conference contributions [3]}, [4]}, two journal papers [1]}, [6]} and the thesis of the author [7]}.
We repeat some of the background, definitions and theorems here for convenience, and for supplying the motivation for the research that led to the third, fourth and fifth decomposition theorem that we state and prove in Section .
